Time-frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with signals having a strong non-stationary characteristic or multi-component signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this study. It is shown that the energy concentration of the timefrequency representation (TFR) of a strong frequency modulated signal from a PCT transform can be further enhanced by a SET transform. The technique can also be employed to accurately extract the signal components of a multi-component nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR which demonstrates the superiority of the current technique in dealing with non-stationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with non-stationary signals from practical sources.